One isn't precluding the other. For example, SBCL is an implementation of Common Lisp that compiles everything ahead-of-time down to native code, and like all Common Lisp implementations, it offers a powerful REPL suited for interactive development. The compiler has low overhead, so you don't even notice that it compiles everything you type into your REPL.

Another common misconception is that AOT compilers can only be used to build libraries/executables, which then get executed. Again, SBCL is an example of an AOT compiler that works at function-level granularity[0], in accordance with Lisp heritage of image-based development, where you write your program by starting it, and then adding/removing/modifying code into a running instance. SBCL achieves this by having the compiler being a part of your application runtime.

I don't know how Julia is implemented internally, but since it's essentially a Lisp clothed in syntax that's more pleasant to the masses, it inherits a lot of Lisp family heritage. That could easily include a fast, to-native, in-process AOT compiler.

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[0] - Or maybe even lower.